DeepAI AI Chat
Log In Sign Up

Interpolating Classifiers Make Few Mistakes

01/28/2021
by   Tengyuan Liang, et al.
0

This paper provides elementary analyses of the regret and generalization of minimum-norm interpolating classifiers (MNIC). The MNIC is the function of smallest Reproducing Kernel Hilbert Space norm that perfectly interpolates a label pattern on a finite data set. We derive a mistake bound for MNIC and a regularized variant that holds for all data sets. This bound follows from elementary properties of matrix inverses. Under the assumption that the data is independently and identically distributed, the mistake bound implies that MNIC generalizes at a rate proportional to the norm of the interpolating solution and inversely proportional to the number of data points. This rate matches similar rates derived for margin classifiers and perceptrons. We derive several plausible generative models where the norm of the interpolating classifier is bounded or grows at a rate sublinear in n. We also show that as long as the population class conditional distributions are sufficiently separable in total variation, then MNIC generalizes with a fast rate.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/22/2019

Fast rates for empirical risk minimization with cadlag losses with bounded sectional variation norm

Empirical risk minimization over sieves of the class F of cadlag functio...
07/22/2019

Fast rates for empirical risk minimization over càdlàg functions with bounded sectional variation norm

Empirical risk minimization over classes functions that are bounded for ...
12/28/2018

Consistency of Interpolation with Laplace Kernels is a High-Dimensional Phenomenon

We show that minimum-norm interpolation in the Reproducing Kernel Hilber...
08/07/2020

Generalization error of minimum weighted norm and kernel interpolation

We study the generalization error of functions that interpolate prescrib...
12/15/2019

On the Generalization Properties of Minimum-norm Solutions for Over-parameterized Neural Network Models

We study the generalization properties of minimum-norm solutions for thr...
12/13/2012

Learning Sparse Low-Threshold Linear Classifiers

We consider the problem of learning a non-negative linear classifier wit...
03/20/2020

Sample Complexity Result for Multi-category Classifiers of Bounded Variation

We control the probability of the uniform deviation between empirical an...